According to the online magazine Before It's News, Cuba celebrates its independence with parades, but there is not a public holiday associated with Cuba's independence. Cuba gained its independence from Spain on May 20, 1902.
The online magazine Folklife in Louisiana notes that those who grew up in Cuba after the 1959 revolution were taught that May 20th is a negative day in Cuba's history because the country was passed from Spanish authority to North American authority. It was not until the end of the 1959 revolution that Cuba became truly independent. Thus, younger generations celebrate the 1959 revolution instead of the country's day of independence.